## Thursday, July 25, 2019

### Entanglement

Suppose two quantum systems, A and B, are perfectly entangled in such a way that for any measurement of one system, the other system must have an exactly corresponding (for simplicity) measurement.

Here’s one causal story that can be given about this that is compatible with both special relativity insofar as it presupposes no preferred reference frame and yet respects the commonplace intuition that there is no backwards causation.

The story assumes that quantum systems can communicate with each other faster than light, but not absolutely temporally backwards. Specifically, if system A at point a in spacetime is not in the future light cone of point b, then system A at a can send a signal to a system at point b. This saves much of the intuition that there is no backwards causation.

Here is what happens in entanglement cases. Suppose you are one of the two systems and you are being measured.

1. You uniformly choose a random real number x between 0 and 1, and send out a superluminal message “I am being measured and I picked x” to the other entangled system to arrive at the time of the other system’s measurement—unless the other system’s measurement is in your future, in which case your message doesn’t arrive.

2. You check for receipt of a superluminal “I am being measured and I picked y” message from the other twin.

3. If you don’t get the message, then you are designated the Boss of the Measurement.

4. If you do get the message, then you are designated the Boss of the Measurement if and only if x > y.

5. If you are designated the Boss of the Measurement, then you now collapse your own state according to the Born rule probabilities, and send a superluminal message “I am the Boss and I collapsed to state z”.

6. If you are not designated the Boss of the Measurement, then you are almost sure to receive a message of the form “I am the Boss and I collapsed to state z”, so you collapse to the entangled state corresponding to the other system’s state z.

The sequence of tasks 1-6 either happens super-fast or they are all temporally simultaneous but explanatorily sequential. Furthermore, the messaging is hidden from us: the choice of the real numbers x and y, the messages sent and Boss status are all hidden variables.

Notes:

A. The setup has a possibility, but with zero probability, of failure—namely, if both systems randomly chose the same number (i.e., x = y), then neither is Boss of the Measurement and collapse doesn’t happen.

B. According to some but not all reference frames the superluminal messaging will result in messages arriving before they are sent (i.e., the receipt is spacelike separated from the sending). But if the superluminal messaging is limited to the above kinds of messages, hopefully one can ensure that causal loops are ruled out, and so no paradox ensues. And there is no absolutely-backwards causation.

C. Locality is violated by the superluminal messaging, of course. But having a causal explanation is more important than ensuring locality.

D. With more than two systems entangled, things get much more complicated.

E. If the entanglement isn’t perfect, things get much more complicated.

Michael Gonzalez said...

I've always wanted to ask someone who knows this stuff better than I do: why are we so concerned with STR's rejection of preferred reference frames when GTR supersedes STR and it doesn't care about reference frames?

I did ask Tim Maudlin about a Bohmian view of QM coupled with a Neo-Lorentzian view of STR, and he gave me some very interesting things to think about. But, I guess I just don't understand why STR is such a concern when GTR replaces it and doesn't have its same issues.... In other words, why not take the so-called "cosmic time" of GTR, and say that the causation is super-fast but still always forward in cosmic time?

Alexander R Pruss said...

GTR doesn't have a privileged simultaneity either. The "cosmic time" is, as far as I know, not well-defined at the local level.

IanS said...

For this approach to work, time would have to have an intrinsic direction – the messages would have to be excluded from the backward (but not the forward) light cone. This may or may not worry you, since collapse style interpretations of QM seem to require a direction of time in any case.

Do you need any new story to preserve causal explanation? Isn’t the experimental setup that produced the entanglement and arranged the measuring apparatus sufficient explanation of the correlations? Note that even without non-locality, QM “explains” e.g. a detector’s propensity to click, but not why it clicked or did not click on any particular occasion. Non-locality merely makes it weirder.

As you say in D, with more than two entangled systems, things get complicated. Most things are entangled, if only very slightly, with many other things. So in reality, there would be a lot of complication.

Alexander R Pruss said...

I think the direction of time comes from the predominant direction of causation.

The causal problem arises in the Bell inequality setting, where there is a correlation between the choice of which quantity to measure at, say, location A, the result of the measurement at A, and the result of the measurement at B. This correlation is difficult to explain causally.

Michael Gonzalez said...

First off, I think it's better to just leave terms like "direction of time" out of it, since so much nonsense is said about that. It's better to just say that states of affairs evolve or that events happen one after another.

And, in any case, I don't think it's difficult to come up with a causal explanation for the Bell-type correlations, as long as you permit superluminal (perhaps even instantaneous) causal influence. My point about GTR before is that it doesn't seem to me to make any reference at all to reference frames (pun intended). Sure, none is privileged in the trivial sense that there aren't any and therefore aren't any privileged ones.... But, then, this is all way above my pay-grade. Lol

Alexander R Pruss said...

The difficulty in explaining Bell-type correlations with superluminal causal influence is to account for the direction of the causality and take into account the symmetry in the setup. We have two measurements at distant locations. There is a correlation between the outcomes of the measurements. But how to explain that correlation? Which of the two measurements triggered the collapse?

On the model in my post, the system randomly chooses one of the two measurements as the trigger.

It now occurs to me that a simpler and more elegant solution would be overdetermination.